Mathematics - Numbers, Symbols and Numbering Systems

Rules Of Exponents Worksheet - Mathematics - Numbers, Symbols and Numbering Systems

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Numbers and Symbols

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Rules Of Exponents Worksheet

Our oldest ancestors already knew how to count, such as the number of items, habitancy or animals. They were whether able to count objects and visualise numbers or were able to surmise the number of objects in a set. For uncomplicated counting, we use basic numbers or cardinal numbers, such as 1, 2, 3, 4 and so on. Serial or ordinal numbers conclude order, such as 1st, 2nd or 3rd.

Numbers and symbols are what mathematics is beyond doubt made of. There are many numerical and symbol systems in the world.

We most often use the decimal system, which is most common. A number in the decimal system (although generally also in other numerical systems) is, by rule, made up of some numbers or digits, where the value of each digit depends on its position in the number. Digits within the decimal system are the Indian symbols for 1 to 0, which were adopted by al-Choresmi for the Arabian mathematical system.

Numbering Systems

Numbers can look quite differently. Some numbers were in wedge shaped form, and Arabian numbers, which originally came from India, also look different. The Romans and the Chinese also used totally separate symbols.

The Roman numbering system is based on the adding system, where there are a certain number of basic numbers and aiding symbols, combined agreeing to some rules to form a number with the aim of using as few number of symbols as possible. Even so, larger numbers under this system are not beyond doubt readable and, with very large numbers, new symbols must be invented.

Under this system, the capital letter of I is used to describe one unit, V to describe five units, X ten and C one hundred.

Therefore, seven would be written as Vii (V+I+I). If a smaller unit symbol is to the left of a larger one, then it is subtracted, such that the number 9 is written as Ix (X-I).

Thirty is written as Xxx and 321 as Cccxxxi (100+100+100+10+10+1).

The present numbering system, where a number's value is described by the number of the digits with their individual positions, has its origin in India. agreeing to this system, the position of a number determines its value. Therefore, for the number 321, the number 1 has a value of 1, the number 2 twenty and the number 3 three hundred.

This system was brought to Europe by the Brit Aderland von Bath in the year 1100.

The present numbering system is based on multiples of ten and use the digits from 1 to 0.

Another numbering system is the binary system. In this system, there are only two value numbers. For example, the number 10101 is read as follows: 1 is one, 0 is two, 1 is four, 0 is eight and 1 sixteen. When we add all these together, we get the number 21 (according to our decimal numbering system).

The symbols 0 and 1 are used to describe the numbers 0 to 9 as well. Under the binary system, the number 9 is represented as 1001. The binary numbering system is read from right to left, starting with the exponent 0. Each digit to the left has one higher exponent number, where the binary symbol representing each digit is multiplied by the number 2, which has a power of the exponent connected with that digit.

The binary numbering system is used mostly in semi-conductor electronics when describing on-off chain states.

Other numbering system use the numbers 5 or 16 as their base.

Below are shown some numbering systems:

Decimal

Symbols: 0,1,2,3,4,5,6,7,8,9

Base:10

Binary

Symbols:0.1

Base: 2

Octal

Symbols: 0,1,2,3,4,5,6,7

Base: 8

Hexadecimal

Symbols: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F

Base: 16

Threescore

Symbols: 0...59

Base: 60

The most discrete of ways to enumerate values have been invented, such as the symbols used by the Romans or the Arabs (Indian).

Numbers can then be classified differently, such as "natural numbers", "rational numbers" or "whole numbers". Each category has its own characteristic which is revealed through its mathematical use.

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